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Chapter 14: Problem 21

It takes \(880 \mathrm{J}\) to raise the temperature of \(350 \mathrm{g}\) of lead from 0 to \(20.0^{\circ} \mathrm{C} .\) What is the specific heat of lead?

Short Answer

Expert verified
Answer: The specific heat of lead is \(0.1257 \frac{\mathrm{J}}{\mathrm{g}\cdot^{\circ}\mathrm{C}}\).

Step by step solution

01

Identify the given values

We are given the following information: - Amount of energy required to raise the temperature (Q) = 880 J - Mass of lead (m) = 350 g - Initial temperature (T1) = 0°C - Final temperature (T2) = 20.0°C
02

Write down the formula for energy change

The formula for energy change, which relates energy, mass, specific heat, and temperature change is: \(Q = mc (T_{2} - T_{1})\) We need to solve for the specific heat of lead (c), so we can rewrite the formula as follows: \(c = \frac{Q}{m(T_{2} - T_{1})}\)
03

Plug in the given values into the formula

Now we can substitute the given values into the equation: \(c = \frac{880 \mathrm{J}}{350 \mathrm{g}(20.0^{\circ}\mathrm{C}-0^{\circ}\mathrm{C})}\)
04

Calculate the specific heat

Simplify and compute the value for the specific heat: \(c = \frac{880 \mathrm{J}}{350 \mathrm{g}(20.0^{\circ}\mathrm{C})}\) \(c = \frac{880 \mathrm{J}}{7000 \mathrm{g}\cdot^{\circ}\mathrm{C}}\) \(c = 0.1257 \frac{\mathrm{J}}{\mathrm{g}\cdot^{\circ}\mathrm{C}}\)
05

Write the final answer

The specific heat of lead is \(0.1257 \frac{\mathrm{J}}{\mathrm{g}\cdot^{\circ}\mathrm{C}}\).

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Most popular questions from this chapter

A \(0.400-\mathrm{kg}\) aluminum teakettle contains \(2.00 \mathrm{kg}\) of water at \(15.0^{\circ} \mathrm{C} .\) How much heat is required to raise the temperature of the water (and kettle) to \(100.0^{\circ} \mathrm{C} ?\)
For a cheetah, \(70.0 \%\) of the energy expended during exertion is internal work done on the cheetah's system and is dissipated within his body; for a dog only \(5.00 \%\) of the energy expended is dissipated within the dog's body. Assume that both animals expend the same total amount of energy during exertion, both have the same heat capacity, and the cheetah is 2.00 times as heavy as the dog. (a) How much higher is the temperature change of the cheetah compared to the temperature change of the dog? (b) If they both start out at an initial temperature of \(35.0^{\circ} \mathrm{C},\) and the cheetah has a temperature of \(40.0^{\circ} \mathrm{C}\) after the exertion, what is the final temperature of the dog? Which animal probably has more endurance? Explain.
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